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Volume 36 (2022): Issue 1 (March 2022)

Volume 35 (2021): Issue 2 (September 2021)

Volume 35 (2021): Issue 1 (February 2021)

Volume 34 (2020): Issue 2 (September 2020)

Volume 34 (2020): Issue 1 (July 2020)

Volume 33 (2019): Issue 1 (September 2019)

Volume 32 (2018): Issue 1 (September 2018)

Volume 31 (2017): Issue 1 (September 2017)

Volume 30 (2016): Issue 1 (September 2016)

Volume 29 (2015): Issue 1 (September 2015)

Journal Details
Format
Journal
eISSN
2391-4238
First Published
01 Jan 1985
Publication timeframe
2 times per year
Languages
English

Search

Volume 30 (2016): Issue 1 (September 2016)

Journal Details
Format
Journal
eISSN
2391-4238
First Published
01 Jan 1985
Publication timeframe
2 times per year
Languages
English

Search

13 Articles
Open Access

On Popoviciu-Ionescu Functional Equation

Published Online: 23 Sep 2016
Page range: 5 - 15

Abstract

Abstract

We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our solution is based on a generalization of Radó’s theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.

Keywords

  • functional equations
  • exponential polynomials on Abelian groups
  • Montel type theorem

MSC 2010

  • 39B22
  • 39A70
  • 39B52
Open Access

Wild Primes of a Higher Degree Self-Equivalence of a Number Field

Published Online: 23 Sep 2016
Page range: 17 - 38

Abstract

Abstract

Let ℓ > 2 be a prime number. Let K be a number field containing a unique ℓ-adic prime and assume that its class is an ℓth power in the class group CK. The main theorem of the paper gives a sufficient condition for a finite set of primes of K to be the wild set of some Hilbert self-equivalence of K of degree ℓ.

Keywords

  • higher degree Hilbert-symbol equivalence
  • wild prime

MSC 2010

  • 11E12
  • 11E81
Open Access

Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Published Online: 23 Sep 2016
Page range: 39 - 62

Abstract

Abstract

Some reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.

Keywords

  • trace class operators
  • Hilbert-Schmidt operators
  • trace
  • convex functions
  • Jensen’s inequality
  • trace inequalities for matrices

MSC 2010

  • 47A63
  • 47A99
Open Access

Random Dynamical Systems with Jumps and with a Function Type Intensity

Published Online: 23 Sep 2016
Page range: 63 - 87

Abstract

Abstract

In paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.

Keywords

  • dynamical systems
  • asymptotic stability
  • Markov operators

MSC 2010

  • 37A30
  • 60J75
  • 93D20
Open Access

Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces

Published Online: 23 Sep 2016
Page range: 89 - 110

Abstract

Abstract

The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known results in the existing literature.

Keywords

  • complex valued metric spaces
  • common fixed points
  • self-maps
  • Cauchy sequence
  • contractive conditions

MSC 2010

  • 47H10
  • 54H25
Open Access

On the Normal Stability of Functional Equations

Published Online: 23 Sep 2016
Page range: 111 - 128

Abstract

Abstract

In the paper two types of stability and of b-stability of functional equations are distinguished.

Keywords

  • Stability
  • normal stability
  • b-stability
  • uniform b-stability
  • normal uniform b-stability
  • restricted uniform b-stability
  • translation equation
  • exponential Cauchy equation
  • Dhombres’ equation
  • sine
  • cosine and quadratic equations
  • squares of Cauchy and Jensen equations
  • Lobachevski’s equation
  • Pexider’s equation

MSC 2010

  • 39B82
  • 39B62
Open Access

Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Published Online: 23 Sep 2016
Page range: 129 - 142

Abstract

Abstract

In this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in [6], that is showing it using conditions generalizing the notion of tightness of measures. In order to do that we use tightness theory for random measures as developed by H. Crauel in [2].

Keywords

  • random dynamical systems
  • invariant measures
  • asymptotic stability

MSC 2010

  • 37H99
  • 37B25
  • 47B80
  • 60H25
Open Access

The Motivic Igusa Zeta Series of Some Hypersurfaces Non-Degenerated with Respect to their Newton Polyhedron

Published Online: 23 Sep 2016
Page range: 143 - 179

Abstract

Abstract

We describe some algorithms, without using resolution of singularities, that establish the rationality of the motivic Igusa zeta series of certain hypersurfaces that are non-degenerated with respect to their Newton polyhedron. This includes, in any characteristic, the motivic rationality for polydiagonal hypersurfaces, vertex singularities, binomial hypersurfaces, and Du Val singularities.

Keywords

  • motivic Igusa zeta series
  • Du Val singularities
  • stationary phase method

MSC 2010

  • 14G10
  • 18F30
Open Access

Alienation of the Jensen, Cauchy and d’Alembert Equations

Published Online: 23 Sep 2016
Page range: 181 - 191

Abstract

Abstract

Let (S, +) be a commutative semigroup, σ : SS be an endomorphism with σ2 = id and let K be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions f, g : SK of the functional equation f(x+y)+f(x+σ(y))+g(x+y)=2f(x)+g(x)g(y)forx,yS.$$f(x + y) + f(x + \sigma (y)) + g(x + y) = 2f(x) + g(x)g(y)\;\;\;\;{\rm for}\;\;x,y \in S.$$ We also consider an analogous problem for the Jensen and the d’Alembert equations as well as for the d’Alembert and the exponential Cauchy equations.

Keywords

  • Alienation
  • exponential Cauchy equation
  • Jensen equation
  • d’Alembert equation

MSC 2010

  • 39B52
  • 39B72
Open Access

Characterizations of Rotundity and Smoothness by Approximate Orthogonalities

Published Online: 23 Sep 2016
Page range: 193 - 201

Abstract

Abstract

In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we provide some new characterizations of rotundity and smoothness of dual spaces.

Keywords

  • approximate orthogonality
  • rotundity
  • smoothness
  • dual space
  • norm derivatives

MSC 2010

  • 46B20
  • 46C50
  • 46B10
Open Access

The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

Published Online: 23 Sep 2016
Page range: 203 - 217

Abstract

Abstract

We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.

Keywords

  • boundary value problems
  • weak solutions
  • second order elliptic linear equations
  • unbounded domains
  • Dini-continuity

MSC 2010

  • 35J25
Open Access

A Note on Additive Groups of Some Specific Associative Rings

Published Online: 23 Sep 2016
Page range: 219 - 229

Abstract

Abstract

Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.

Keywords

  • -groups
  • ideals
  • associative rings

MSC 2010

  • 20K99
Open Access

Report of Meeting

Published Online: 23 Sep 2016
Page range: 231 - 249

Abstract

13 Articles
Open Access

On Popoviciu-Ionescu Functional Equation

Published Online: 23 Sep 2016
Page range: 5 - 15

Abstract

Abstract

We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our solution is based on a generalization of Radó’s theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.

Keywords

  • functional equations
  • exponential polynomials on Abelian groups
  • Montel type theorem

MSC 2010

  • 39B22
  • 39A70
  • 39B52
Open Access

Wild Primes of a Higher Degree Self-Equivalence of a Number Field

Published Online: 23 Sep 2016
Page range: 17 - 38

Abstract

Abstract

Let ℓ > 2 be a prime number. Let K be a number field containing a unique ℓ-adic prime and assume that its class is an ℓth power in the class group CK. The main theorem of the paper gives a sufficient condition for a finite set of primes of K to be the wild set of some Hilbert self-equivalence of K of degree ℓ.

Keywords

  • higher degree Hilbert-symbol equivalence
  • wild prime

MSC 2010

  • 11E12
  • 11E81
Open Access

Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Published Online: 23 Sep 2016
Page range: 39 - 62

Abstract

Abstract

Some reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.

Keywords

  • trace class operators
  • Hilbert-Schmidt operators
  • trace
  • convex functions
  • Jensen’s inequality
  • trace inequalities for matrices

MSC 2010

  • 47A63
  • 47A99
Open Access

Random Dynamical Systems with Jumps and with a Function Type Intensity

Published Online: 23 Sep 2016
Page range: 63 - 87

Abstract

Abstract

In paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.

Keywords

  • dynamical systems
  • asymptotic stability
  • Markov operators

MSC 2010

  • 37A30
  • 60J75
  • 93D20
Open Access

Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces

Published Online: 23 Sep 2016
Page range: 89 - 110

Abstract

Abstract

The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known results in the existing literature.

Keywords

  • complex valued metric spaces
  • common fixed points
  • self-maps
  • Cauchy sequence
  • contractive conditions

MSC 2010

  • 47H10
  • 54H25
Open Access

On the Normal Stability of Functional Equations

Published Online: 23 Sep 2016
Page range: 111 - 128

Abstract

Abstract

In the paper two types of stability and of b-stability of functional equations are distinguished.

Keywords

  • Stability
  • normal stability
  • b-stability
  • uniform b-stability
  • normal uniform b-stability
  • restricted uniform b-stability
  • translation equation
  • exponential Cauchy equation
  • Dhombres’ equation
  • sine
  • cosine and quadratic equations
  • squares of Cauchy and Jensen equations
  • Lobachevski’s equation
  • Pexider’s equation

MSC 2010

  • 39B82
  • 39B62
Open Access

Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Published Online: 23 Sep 2016
Page range: 129 - 142

Abstract

Abstract

In this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in [6], that is showing it using conditions generalizing the notion of tightness of measures. In order to do that we use tightness theory for random measures as developed by H. Crauel in [2].

Keywords

  • random dynamical systems
  • invariant measures
  • asymptotic stability

MSC 2010

  • 37H99
  • 37B25
  • 47B80
  • 60H25
Open Access

The Motivic Igusa Zeta Series of Some Hypersurfaces Non-Degenerated with Respect to their Newton Polyhedron

Published Online: 23 Sep 2016
Page range: 143 - 179

Abstract

Abstract

We describe some algorithms, without using resolution of singularities, that establish the rationality of the motivic Igusa zeta series of certain hypersurfaces that are non-degenerated with respect to their Newton polyhedron. This includes, in any characteristic, the motivic rationality for polydiagonal hypersurfaces, vertex singularities, binomial hypersurfaces, and Du Val singularities.

Keywords

  • motivic Igusa zeta series
  • Du Val singularities
  • stationary phase method

MSC 2010

  • 14G10
  • 18F30
Open Access

Alienation of the Jensen, Cauchy and d’Alembert Equations

Published Online: 23 Sep 2016
Page range: 181 - 191

Abstract

Abstract

Let (S, +) be a commutative semigroup, σ : SS be an endomorphism with σ2 = id and let K be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions f, g : SK of the functional equation f(x+y)+f(x+σ(y))+g(x+y)=2f(x)+g(x)g(y)forx,yS.$$f(x + y) + f(x + \sigma (y)) + g(x + y) = 2f(x) + g(x)g(y)\;\;\;\;{\rm for}\;\;x,y \in S.$$ We also consider an analogous problem for the Jensen and the d’Alembert equations as well as for the d’Alembert and the exponential Cauchy equations.

Keywords

  • Alienation
  • exponential Cauchy equation
  • Jensen equation
  • d’Alembert equation

MSC 2010

  • 39B52
  • 39B72
Open Access

Characterizations of Rotundity and Smoothness by Approximate Orthogonalities

Published Online: 23 Sep 2016
Page range: 193 - 201

Abstract

Abstract

In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we provide some new characterizations of rotundity and smoothness of dual spaces.

Keywords

  • approximate orthogonality
  • rotundity
  • smoothness
  • dual space
  • norm derivatives

MSC 2010

  • 46B20
  • 46C50
  • 46B10
Open Access

The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

Published Online: 23 Sep 2016
Page range: 203 - 217

Abstract

Abstract

We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.

Keywords

  • boundary value problems
  • weak solutions
  • second order elliptic linear equations
  • unbounded domains
  • Dini-continuity

MSC 2010

  • 35J25
Open Access

A Note on Additive Groups of Some Specific Associative Rings

Published Online: 23 Sep 2016
Page range: 219 - 229

Abstract

Abstract

Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.

Keywords

  • -groups
  • ideals
  • associative rings

MSC 2010

  • 20K99
Open Access

Report of Meeting

Published Online: 23 Sep 2016
Page range: 231 - 249

Abstract

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